Method and system for optimizing the arrangement of spatial elements

ABSTRACT

In a data visualization system, a method of analyzing and representing spatial data sets to optimize the arrangement of spatial elements, the method including the steps of: retrieving data from a data storage module that is in communication with the data visualization system, determining lift values for a plurality of predefined spatial areas from the retrieved data based on a set of fuzzy association rules applied to the predefined spatial areas, determining spatial performance values for the predefined spatial areas, and calculating a weighted spatial relationship between the determined lift values and spatial performance values.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.13/516,136, filed 26 Dec. 2012, which is a National Stage Application ofPCT/NZ2010/000252, filed 14 Dec. 2010, which claims benefit of U.S.Provisional Ser. No. 61/286,029, filed 14 Dec. 2009 and whichapplications are incorporated herein by reference. To the extentappropriate, a claim of priority is made to each of the above disclosedapplications.

FIELD OF THE INVENTION

The present invention relates to a method and system for optimizing thearrangement of spatial elements.

BACKGROUND

Market basket analysis is used to determine relationships betweendifferent transaction items based on analysing which transaction itemsare usually combined together. It is known to produce individual rulesthat can be constructed to determine relationships. These relationshipsmay also extend to the inclusion of spatial relationships that take intoaccount the relative spatial separation or closeness of the transactionitems.

An object of the present invention is to provide an improved method andsystem for representing spatial association rules.

A further object of the present invention is to provide an improvedmethod and system for applying spatial association rules in conjunctionwith a spatial performance model in order to optimize a spatialsolution.

Each object is to be read disjunctively with the object of at leastproviding the public with a useful choice.

The present invention aims to overcome, or at least alleviate, some orall of the afore-mentioned problems.

SUMMARY OF THE INVENTION

The present invention provides a system and method that optimizes thespatial arrangement of elements.

According to one aspect, the present invention provides, in a datavisualization system, a method of analysing and representing spatialdata sets to optimize spatial layouts, the method including the stepsof: retrieving data from a data storage module that is in communicationwith the data visualization system, determining lift values for aplurality of predefined spatial areas from the retrieved data based on aset of fuzzy association rules applied to the predefined spatial areas,determining spatial performance values for the predefined spatial areas,calculating a weighted spatial relationship between the determined liftvalues and spatial performance values.

Preferably the fuzzy association rules apply spatial data within theretrieved data to a set of association rules to determine lift valuesfor the predefined spatial areas.

Preferably, the method includes the steps of monitoring the retrieveddata over time and predicting changes to the weighted spatialrelationships based on changes in the retrieved data.

Preferably, the method includes the steps of applying a geneticalgorithm to the retrieved data to form a spatial design, andsubsequently performing the determination and calculation steps.

Preferably, the method includes the steps of determining isolatedspatial areas and calculating weighted spatial relationships within theisolated spatial area.

According to a further aspect, the present invention provides a datavisualization system that is arranged to perform the herein describedmethods.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way ofexample only, with reference to the accompanying drawings, in which:

FIG. 1 shows a conceptual system block diagram according to anembodiment of the present invention;

FIG. 2 shows a graph illustrating a rule where as distance is doubledthe weight is increased by four times according to an embodiment of thepresent invention;

FIG. 3 shows a system block diagram of a gaming environment according toan embodiment of the present invention;

FIG. 4 shows a table displaying the results of a method according to anembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

First Embodiment

Embodiments of the present invention are provided herein to describe howthe use of market basket analysis may be extended to data sets includinga vast amount of numerical data, such as that produced by the manyinteractions between gaming devices, for example.

Embodiments of the present invention are described herein with referenceto a system adapted or arranged to perform a method of applying spatialassociation rules in conjunction with a spatial performance model inorder to optimize a spatial solution.

In summary, the system includes at least a processor, one or more memorydevices or an interface for connection to one or more memory devices,input and output interfaces for connection to external devices in orderto enable the system to receive and operate upon instructions from oneor more users or external systems, a data bus for internal and externalcommunications between the various components, and a suitable powersupply. Further, the system may include one or more communicationdevices (wired or wireless) for communicating with external and internaldevices, and one or more input/output devices, such as a display,pointing device, keyboard or printing device.

The processor is arranged to perform the steps of a program stored asprogram instructions within the memory device. The program instructionsenable the various methods of performing the invention as describedherein to be performed. The program instructions may be developed orimplemented using any suitable software programming language andtoolkit, such as, for example, a C-based language. Further, the programinstructions may be stored in any suitable manner such that they can betransferred to the memory device or read by the processor, such as, forexample, being stored on a computer readable medium. The computerreadable medium may be any suitable medium, such as, for example, solidstate memory, magnetic tape, a compact disc (CD-ROM or CD-R/W), memorycard, flash memory, optical disc, magnetic disc or any other suitablecomputer readable medium.

The system is arranged to be in communication with external data storagesystems or devices in order to retrieve the relevant data.

It will be understood that the system herein described includes one ormore elements that are arranged to perform the various functions andmethods as described herein. The following portion of the description isaimed at providing the reader with an example of a conceptual view ofhow various modules and/or engines that make up the elements of thesystem may be interconnected to enable the functions to be implemented.Further, the following portion of the description explains in systemrelated detail how the steps of the herein described method may beperformed. The conceptual diagrams are provided to indicate to thereader how the various data elements are processed at different stagesby the various different modules and/or engines.

It will be understood that the arrangement and construction of themodules or engines used to implement the methods described may beadapted accordingly depending on system and user requirements so thatvarious functions may be performed by different modules or engines tothose described herein, and that certain modules or engines may becombined into single modules or engines.

It will be understood that the modules and/or engines used to implementthe methods described may be implemented and provided with instructionsusing any suitable form of technology. For example, the modules orengines may be implemented or created using any suitable software codewritten in any suitable language, where the code is then compiled toproduce an executable program that may be run on any suitable computingsystem. Alternatively, or in conjunction with the executable program,the modules or engines may be implemented using any suitable mixture ofhardware, firmware and software. For example, portions of the modulesmay be implemented using an application specific integrated circuit(ASIC), a system-on-a-chip (SoC), field programmable gate arrays (FPGA)or any other suitable adaptable or programmable processing device.

Although the herein described embodiments are directed towards applyingthe methodology to gaming data obtained from a gaming system, it will beunderstood that these methods may be applied to other scenarios andsystems.

The methods described herein may be implemented using a general purposecomputing system specifically programmed to perform the described steps.Alternatively, the methods described herein may be implemented using aspecific computer system such as a data visualization computer, adatabase query computer, a graphical analysis computer, a retailenvironment analysis computer, a gaming data analysis computer, amanufacturing data analysis computer, a business intelligence computeretc., where the computer has been specifically adapted to perform thedescribed steps on specific data captured from an environment associatedwith a particular field.

For example, the data provided as an input to the system may be of anysuitable type of data, for example, real world data including, but notlimited to, gaming or gambling data associated with a gaming environmentsuch as a casino, event data, test or quality control data obtained froma manufacturing environment, business data retrieved from an accountingsystem, sales data retrieved from a company database, etc. All this datamay be received by the system in real time in a cache memory or may bestored in a more permanent manner.

According to this embodiment, as shown in FIG. 1, the data is retrievedfrom a data storage module 101 by a data retrieval module 103. The dataretrieval module 103 provides this data to the various other engines andmodules of the system to enable the various methodologies to beperformed.

This embodiment is directed towards analyzing gaming data for thepurpose of gaming floor analysis in a casino environment. In particular,the description describes methods utilized by various modules andengines for creating fuzzy spatial association rules and gravitymodeling. It will be understood that other analytical building blocks(modules and engines for example) may be used to decode theinteractions; these may include, for example, visual representationmodules, experimental design modules, mini casino management modules andsocial network analysis modules.

Although a vast amount of data is readily available from a gamingenvironment for analysis, it is usually not put to good use where theanalysis of the data leads to successful planning and the maximizationof profits due to gaming asset arrangement.

By including other non spatial drivers to the data sets being analyzed,for example measuring the lift values from a marketing campaign, stepsare made in the right direction to lead to successful planning.

The next step utilizes a spatial association rules (sAR) module 105 inconjunction with an association rules engine 107 to build models thatcan be used to drive yield to specific areas of the gaming floor atspecific times of day. That is, by looking at association rules based onboth time of use of gaming assets and the location of the gaming assetsin the gaming environment, further insight is obtained.

The rules developed and implemented by the spatial association rules(sAR) module and association rules engine offer a way of disentanglingthe vast dynamics of the gaming floor into a series of statisticallyassociated patterns. The output of the analysis then enables a user touse the associations to rearrange the gaming floor and possibly pushactivity to areas of interest.

Further, the data from the retrieval module is communicated to a spatialperformance module 109. The spatial performance module determines valuesassociated with various spatial elements inside a defined space. Forexample, an average of a specific value may be determined for allelements within a defined space.

The output of the spatial performance module and spatial associationrules (sAR) module is communicated to an analysis module 111, whichdetermines the relationship between the two outputs. That is, theanalysis module determines how the spatial performance values for thespatial elements and the relationship values for those spatial elementsare related to each other.

The output from the analysis module is provided to a rendering module113 which in turn provides a rendered output to an output module 115 inthe form of a graphical representation showing the associations betweenthe different elements (e.g. gaming assets and associated transactions)being analyzed. The output module in this embodiment is a displaymodule.

As an alternative to, or in conjunction with, the display module,further output modules may be provided to output the associationresults. The output data is provided to the display and/or furtheroutput modules to enable a user to visualize the raw data in a mannerthat conveys more useful or hidden information that would otherwise belost.

The further output module may be a printing device in communication withthe described system to receive print control data so thatrepresentations of the data may be printed on any suitable print medium.Alternatively, the further output module may be an interface thatenables the output data to be interfaced with other data handlingmodules or storage devices. As a further alternative, the output modulemay be the same or different data storage module as described herein.

Spatial association rules (sAR) are association rules that involve aspatial variable (see P. Laube, M. de Berg, M. van Kreveld (2008).Headway in Spatial Data Handling (Eds. Anne Ruas, Christopher Gold),Lecture Notes in Geoinformation and Cartography Series, pp. 575-593) andresult in a lift measurement.

A lift measurement is a statistical measurement defined as follows:Lift(A→C)=P(A∩C)/P(A)P(C)Lift (A→C)=probability that A and C occur together, divided by the sameprobability assuming A and C to be independent.

The most common spatial variable is distance. In terms of a gamingenvironment, the association rules establish the effective lift that onegame has on another taking into account the distance between the gamingassets. That is, the effective lift identifies whether one game ishaving an effect on another game's performance. In other words, themarket baskets are weighted by the effect of distance, so that gamingassets that are spatially distant have less of an influence. Thisapproach of using a weighted score is implemented by a fuzzy sAR modulewhich provides as an output a fuzzy measurement of the associationeffect.

The following describes how the Fuzzy Association is defined.

In market basket analysis (MBA), spatial data requires additionalprocessing. Consider the hypothesis that on a casino floor games thatare close to an entrance get more business than those further away. Thequality of the association rules produced by MBA is evaluated in termsof its support and confidence values. The support value of anassociation rule in the case of binary variables (a binary value is ayes or no value, e.g. did someone play a certain slot game or not?) isdefined as the probability that someone buys one product with another(e.g., a customer takes a hotel room and plays on a particular tablegame). The confidence value is the conditional probability, if someonebuys one product, then they buy the other product (see Bart Lewin, A. K.Singh, Andrew Cardno. Let's Talk Turkey: Applying Retail Market BasketAnalysis to Gaming. Casino Enterprise Management, December 2008).

Because the number of possible distances from an entrance is unlimited,calculating these values for MBA requires the use of a threshold and acut-off point to obtain meaningful support and confidence values.

This threshold requirement also arises in other situations; the term‘high coin in’ also requires a cut-off point. There is some literatureavailable on the use of fuzzy logic describing this type of calculation(see L. Zadeh, (1965). Fuzzy sets, Information Control Vol., pp.338-353), where a continuous variable (e.g., coin in) is mapped to ascore in the range [0,1]. Once distances have been converted to theircorresponding scores, the spatial (locations) support and confidencevalues can be calculated by the fuzzy sAR module as follows.

${{Spatial}\mspace{14mu}{{support}\left( {A->C} \right)}} = \frac{\sum\limits_{x}^{\;}{{{score}_{A}(x)} \times {{score}_{C}(x)}}}{n}$${{Spatial}\mspace{14mu}{{confidence}\left( {A->C} \right)}} = \frac{\sum\limits_{x}^{\;}{{{score}_{A}(x)} \times {{score}_{C}(x)}}}{\sum\limits_{x}^{\;}{{score}_{A}(x)}}$

Table 1 shows a simulated example of Spatial Market Basket Analysiscalculations in which weekly coin-in (CI) values for 20 slot games on acasino floor along with distances of the slot games from the closestentrance (D1) and exit (D2) are given. In this example, two spatialassociation rules (sAR) are being compared:

-   sAR1: If A1 then C (notation: A1→C)-   sAR2: If A2 then C (notation: A2→C)-   where the antecedents of the two sAR's (A1 and A2) are:-   A1=slot game is close to an entrance, A2=slot game is close to an    exit-   and the common consequent of the two rules is:-   C=slot game has high weekly coin-in.-   Sp=Spatial support value. Sc=Spatial confidence value.

TABLE 1 Simulated example showing calculations of Spatial Support andSpatial Confidence of the two rules A1→C and A2→C Sp Sp D1 CI Sc (D1) Sc(CI) (A1→C) D2 Sc (D2) (A2→C) 6 75168 1 0.93 0.93 1 0.5 0.47 6 75722 1 11 1 0.5 0.5 6 73807 1 0.76 0.76 1 0.5 0.38 6 74755 1 0.88 0.88 1 0.50.44 7 72183 0.8 0.56 0.45 0 1 0.56 7 72620 0.8 0.61 0.49 0 1 0.61 772325 0.8 0.58 0.46 0 1 0.58 7 71671 0.8 0.49 0.4 0 1 0.49 7 75574 0.80.98 0.79 0 1 0.98 7 74075 0.8 0.79 0.64 0 1 0.79 7 72602 0.8 0.61 0.490 1 0.61 7 72348 0.8 0.58 0.46 0 1 0.58 6 73694 1 0.75 0.75 1 0.5 0.37 673575 1 0.73 0.73 1 0.5 0.37 6 74207 1 0.81 0.81 1 0.5 0.41 6 73868 10.77 0.77 1 0.5 0.38 11 68988 0 0.16 0 2 0 0 11 68462 0 0.09 0 2 0 0 1169014 0 0.16 0 2 0 0 11 68411 0 0.09 0 2 0 0 Sum 14.4 10.81 12 8.52 SARConfidence (A1→C) 0.75 (A2→C) 0.71

According to a further example, the support and confidence values forbuildings being in close proximity to a lake and being above aparticular price threshold are determined as follows:

-   P(Close)=3/7, P(Expensive)=4/7,-   P (Close∩Expensive)=3/7-   Support(Close    Expensive)=P (Close∩Expensive)=3/7=0.43-   Confidence(Close    Expensive)=P (Close∩Expensive)/P(Close)=(3/7)/(3/7)=1

Therefore, the lift value may be calculated as follows:Lift(Close

Expensive)=P (Close∩Expensive)/[P(Close)×P(Expensive)]=(3/7)/[(3/7)×(4/7)]=1.75

The effect of the fuzzy spatial association may be considered for twoslot machines. Lift values may be derived from confidence values (suchas those shown in the above table). The first slot machine with a highlift (H) value from surrounding games the second slot machine with a lowlift (L) value. It is likely that a machine with the high lift value isplayed at the same time as the surrounding games while the machine withthe low lift value is played at different times, which results in areverse kind of dependence.

This can be taken to another level by enabling the spatial performancemodule 109 to calculate the expected game performance of each location.One effective way of calculating the game performance is to build aweighted ranking of the performance of each location. In order to dothis a method of generating the “average” performance of an area isimplemented by the spatial performance module. This average performanceis the summation of the effect of all surrounding games where games thatare further away have less effect on the performance location ranking.In order to do this, inverse distance weighted (see Edward H. Isaaks, R.Mohan Srivastava (1989). Applied Geostatistics, Oxford University Press)performance location or gravity modeling is implemented by the spatialperformance module.

For example, the calculation could be based on the rule that as thedistance is doubled the weight increases by four times. FIG. 2 is anillustration of a graph which shows the effect of this calculation. Asreferred to at http://en.wikipedia.org/wiki/Inverse-square_law, this“inverse-square law generally applies when some force, energy, or otherconserved quantity is radiated outward radially from a source. Since thesurface area of a sphere (which is 4πr²) is proportional to the squareof the radius, as the emitted radiation gets farther from the source, itmust spread out over an area that is proportional to the square of thedistance from the source”. This effect when applied to the “emanation”of performance from a location can be very effectively used to calculatethe impact of one location on another.

It will be understood that other suitable weighting rules may be appliedas an alternative.

The next step performed is by the spatial performance module 109 whichdetermines the spatial performance values by calculating the sum of therank multiplied by the location weight, where the sum of the weights isone (so each weight is the percentage of the total weight). In ageographic sense this calculation follows a model called Shepard'sMethod:

-   -   “The simplest form of inverse distance weighted interpolation is        sometimes called “Shepard's method” (Shepard 1968). The equation        used is as follows:

${F\left( {x,y} \right)} = {\sum\limits_{i - 1}^{n}{w_{i}f_{i}}}$

-   -   where n is the number of scatter points in the set, f_(i) are        the prescribed function values at the scatter points (e.g. the        data set values), and w_(i) are the weight functions assigned to        each scatter point. The classical form of the weight function        is:

$w_{i} = \frac{h_{i}^{- p}}{\sum\limits_{j - 1}^{n}h_{j}^{- p}}$

-   -   where p is an arbitrary positive value”; in the case of gravity        modeling p=2.

Using the spatial performance module to calculate this value for eachgaming machine on the gaming floor results in an average value for eachlocation where it is the weighted sum of the effect of surroundinglocations.

Note: This calculation results in one calculation for the number ofgaming devices squared. So if a gaming floor with 2000 games is beinganalyzed four million calculations will be needed to complete theinteraction analysis.

By combining the gravity model (i.e. calculating the spatial performancevalues) and fuzzy spatial association rules (i.e. calculating the liftvalues) methods within the analysis module 111, a very interestingbreakout of the games on the gaming floor into four interestingcategories (average performance games are not considered interesting) asillustrated by the following table is provided.

High Lift Low Lift Above Expected Leaders Loners Below Expected LaggardsLosers

The spatial performance values and lift values are cross-tabulated toproduce the output, which is a weighted spatial relationship of the liftvalues and spatial performance values. Although the above table showsfour quadrants, it will be understood that these four quadrants aredefining the four general types associated with elements as calculatedby the above described method.

The resultant table of cross-tabulated lift and spatial performancevalues may consist of more than four sections. That is, the resultanttable may have a plurality of columns and a plurality of rows with eachcross section of a column and row relating to a specific lift range orvalue and a specific spatial performance range or value.

Each of the elements being monitored by the system may be entered in aspecific location within the table to indicate whereabouts it fits inwith other elements in relation to their lift and spatial performancevalues. The relative location of each of the elements enables a user todetermine important properties of those elements.

This simple breakout of games is a powerful first step in the dataexploration process. The following section describes the four categoriesof gaming device that result from this combination of the ocean ofinteractions.

The games termed “Leaders” are outperforming the surrounding games andlift the surrounding games. These games may be the leaders in the area.They are often star performers and players may be drawn to these gamesand then flow onto play other games in the same area. Leaders are greatcandidates for further building the characteristics of a specific areaof the gaming floor. They are natural candidates for further marketbasket analysis as they can be used as a draw card for other games thatplayers who like the Leaders show a preference for.

The games termed “Loners” are beacons of performance that are drawingplay but not lifting the games in the immediate area. Consider actionssuch as adding more of the same game or running market basket analysisto find other products that players who play this game like to flowonto. Comparison of the demographics of the players “Loner” game to itsneighbors will give insight into why players in the area are not mixing.

The following describes an example from a real gaming floor. In thisreal world gaming floor optimization there was a salt and pepperarrangement of two games in a bank of slot machines (Alternatingthemes). Both of these themes were giving similar theoretical winnumbers but on further analysis the players were found to be not mixingproducts. Analysis into the demographics of the two games showed thatthe two groups of players were of quite different demographic profiles.The very profitable response to this insight was the creation of twoareas of gaming, one for players who preferred “salt” themes and one forplayers who preferred “pepper” themes. The results were stronger playfor both games, the cost was a move of an existing product and a simplecommunication to the two customer groups informing them where theirgames were now located.

The laggards are games that have a positive lift effect on the gamesaround them but are given play that is less than the surrounding games.The linkage these games have with their surroundings indicates we shouldtreat them with care; one approach is to apply a “Why We Buy” (see WhyWe Buy, Puco Underhill 2000) survey to gain some understanding of theway players are playing these games; questions such as “are weoversupplied with this product in this area”, or “Is the game pricedcorrectly” should be considered in the first round of follow upanalyses.

Games termed “Losers” are the games that have a negative effect on thesurrounding areas and are under performing. This kind of game is a greatcandidate for removal, but one should not jump to conclusions, Sometimesfurther analysis using a market basket approach can show clusters ofthese games that have quite isolated players.

If the players are isolated to a particular product then it might bebetter to setup a separate playing area focused on this small group. Inone real world example it was found that a group of Keno machines thatwere low performers had low (in fact near zero) lift on the surroundinggames. However customer surveys showed the players were extremely loyalto this product. Instead of removing the product one of the mostisolated and underperforming areas was turned into a specialist Kenoroom, this accompanied by a marketing program inviting these players totheir special area was successful; moreover, the space that was madeavailable became one of the highest performing space on the floor.

Often times the gaming floor can be seen as a mass of bright lights andcolors, applying these techniques introduces an analytical frameworkthat can change the way you see a gaming floor. In today's world ofoften diminishing returns, adapting the floor to give customers whatthey want where they want is rapidly becoming a science. The challengelies in that there are ever more products and increasing flexibility,and vastly increasing volumes of data collected from the gaming floor.Operators can either exploit the data and learn to utilize our new foundflexibility, or choose to rely on luck.

The optimization methods described herein may be implemented for usewith a geospatial slowly changing dimension manager that handles thechanging of spatially located data over time. This geospatial dimensionmanager utilizes in-database spatial database management techniques. Adatabase is stored in the memory of the system, such as within the datastorage module, for example. The data may be rendered and displayed toshow the spatial arrangement of the elements associated with the data.

For example, the data may be associated with gaming assets, and theposition of those gaming assets within a gaming environment may berepresented graphically. Where those gaming assets are located onseveral floors, different layers may be used to indicate the floor onwhich the asset is located. Vectors may be used to visually representthe asset and the data being represented.

It will be understood that the spatial data may relate to elements otherthan gaming assets. For example, the data may relate to a manufacturingenvironment, retail store, logistical system, telecommunications networketc, wherein the elements may relate to manufacturing elements, retailelements, logistics elements, telecommunications elements.

The dimension manager may be used to analyse how changes in the spatialarrangement of the elements in the spatial area can affect performanceover time. Various techniques may be implemented using the dimensionmanager. For example, neural networks, such as back propagation networksmay be used. Further, classification type methods or regression analysismay be performed. These methods enable the behavior of the environmentand the elements therein to be predicted by the system.

According to a further example, a genetic algorithm module may be usedto implement a genetic algorithm to build one or more designs. That is,a design that defines a space or layout of various elements may beproduced by a genetic algorithm. Subsequently, the association rules maybe applied in order to forecast the performance of a design, orcombinations of designs. That is, the genetic algorithm may be used todefine a spatial relationship between various elements in a spatialarea. Upon completion of the genetic algorithm, the spatial associationrules may be applied to determine how the defined arrangement performsover time. This enables the system to provide a user with usefuldetailed predictions for new designs prior to implementing the designsin a real life environment.

It will be understood that the models described above may be implementedgenerally over a large space (layout) or may be directed to smallerdefined areas. For example, the system may be used to monitor thespatial area to determine if there are any isolated areas. That is, anisolated area is where measured interactions are isolated to thatparticular area and do not cross over into other areas. For example, ina gaming environment, an isolated area may be a poker environment inwhich customers only attend poker tables, machines and tournamentswithout visiting other areas of the gaming environment. The monitoringof users using recognition techniques enables the system to determinewhether there is any cross over. Recognition techniques include physicalrecognition techniques (e.g. face, voice, gait etc), transactionalrecognition techniques (e.g. bank accounts, loyalty cards etc) or anyother form of recognition technique.

Once the system has determined the isolated area, the optimizationmodels discussed herein may be applied to those separate areas.

FIG. 3 shows an example of how the herein described system may beincorporated within a gaming environment. The gaming environmentconsists of a number of gaming machines 1101 and electronic tables 1103(among other electronic gaming devices) that are adapted to communicateelectronically with other systems using any suitable protocols, such asdata packet protocols.

The gaming environment further includes a number of electronic cashierdevices 1105 and ATMs 1107 which are in communication via a Wide AreaNetwork 1109 with one or more financial databases 1111.

Data from the gaming machines 1101 and electronic tables 1103 aretransferred to a reward program database 1113 and customer database1115. It will be understood that these two databases may be combinedinto a single database.

Data from the cashier devices are also transferred to the reward programdatabase 1113 and customer database 1115. The databases 1113 and 1115are in communication with a central hotel management system 1117 thatoversees the operation of the gaming environment, including theactivities of customers in other areas of a casino, such as shops,hotels, spas etc.

The system 1119 described herein is in communication with the rewardprogram database 1113, customer database 1115 and central hotelmanagement system 1117 so the system can retrieve all necessary dataabout the activities within the gaming environment. The variousembodiments as described herein are employed by the system 1119 toprovide an output 1121.

FIG. 4 shows a further example of a set of tabulated results producedusing the above described methods. The basic four quadrants are shownindicating high lift, low lift, above expected and below expectedvalues. Each of these four quadrants is broken down into a 4×4 cellarrangement in which individual spatial elements (e.g. gaming machines)are placed using, in this example, an ‘X’ or cross. It will beunderstood that the spatial elements may also be defined by anidentification number or symbol rather than a ‘X’. The relative locationof each element in the cell identifies whether that element is a Leader,Laggard, Loner or Loser as defined above as well as providing a finerdefinition within each of the broader definitions based on the locationwithin the 16 cells within each quadrant.

The herein described methods effectively provide a type of quartalanalysis where the analysis focuses on each of the herein describedmethods (gravity modeling, spatial association rules, fuzzy rules)separately. That is, quartal analysis involves arranging variablesassociated with the different analyses in n dimensions, where the datapoints represent n or more variables associated with the analyses. Thequartal method then ranks a set of data points with respect to a firstaxis using a first variable; and based on a second variable, distributesthe set of data points along the first axis while retaining informationrelating to the ranking of data points determined in the ranking stage.This becomes particularly useful where the data points are ranked withrespect to one or more further axes using one or more variables; andthen data points are distributed along the further axes while retaininginformation relating to the ranking of the data points for those furtheraxes.

Therefore, the method described herein analyses and represents spatialdata sets in order to optimize the arrangement of spatial elements whichthe data sets relate to. Data from the data sets is first retrieved froma data storage module. Lift values are then determined for a number ofpredefined spatial areas. That is, interaction relationships betweenspatial elements in various spatial areas are determined using fuzzyassociation rules.

Also, spatial performance values for the predefined spatial areas arealso determined. That is, the performance values of the spatial elementswithin each of the spatial areas are monitored and recorded.

The lift values and spatial performance values are then combined inorder to show or visualise the relationship between each of the spatialelements in a tabulated form.

It will be understood that the methods may equally be applied to asocial networking environment. Further, it will be understood that therelative distance measurements may be a graph distance.

Further Embodiments

It will be understood that the embodiments of the present inventiondescribed herein are by way of example only, and that various changesand modifications may be made without departing from the scope ofinvention.

The invention claimed is:
 1. In a data visualization system, executableon an electronic computing device, a method of analyzing andrepresenting spatial data sets to optimize the arrangement of spatialelements which the data sets relate to, the representation enabling auser to visualize the spatial data sets in a manner that conveysinformation that would otherwise be lost, the method including the stepsof: retrieving data associated with the spatial data sets from a datastorage module that is in communication with the data visualizationsystem; calculating a weight ranking of the performance of each of aplurality of predefined spatial areas; determining lift values for theplurality of predefined spatial areas from the retrieved data using theweight ranking; determining spatial performance values for thepredefined spatial areas; combining the determined lift values andspatial performance values to show the relationship between each of thespatial elements within the predefined spatial areas; and displaying ona display device a graphical representation showing the predefinedspatial areas, by: rendering a rendered output including the graphicalrepresentation showing the relationship between each of the spatialelements within the predefined spatial areas; and providing the renderedoutput to the display device and generating the graphical representationon the display device to allow the user to visualize the data.
 2. Themethod of claim 1 wherein the fuzzy association rules apply spatial datawithin the retrieved data to a set of association rules to determinelift values for the predefined spatial areas.
 3. The method of claim 1further including the steps of monitoring the retrieved data over timeand predicting changes to the weighted spatial relationships based onchanges in the retrieved data.
 4. The method of claim 1 furtherincluding the steps of applying a genetic algorithm to the retrieveddata to form a spatial design, and subsequently performing thedetermination and combining steps.
 5. The method of claim 1 furtherincluding the steps of determining isolated spatial areas andcalculating weighted spatial relationships within the isolated spatialarea.
 6. The method of claim 1 further including the steps of crosstabulating the determined lift values and spatial performance values toshow the relationship between each of the spatial elements within thepredefined spatial areas.
 7. A data visualization system comprising anelectronic computing device including at least one processor and one ormore memory devices, the one or more memory devices storing instructionsexecutable by the at least one processor to perform the method accordingto claim
 1. 8. The data visualization system of claim 7 wherein thefuzzy association rules apply spatial data within the retrieved data toa set of association rules to determine lift values for the predefinedspatial areas.
 9. The data visualization system of claim 7 furtherarranged to perform the steps of monitoring the retrieved data over timeand predicting changes to the weighted spatial relationships based onchanges in the retrieved data.
 10. The data visualization system ofclaim 7 further arranged to perform the steps of applying a geneticalgorithm to the retrieved data to form a spatial design, andsubsequently performing the determination and combining steps.
 11. Thedata visualization system of claim 7 further arranged to perform thesteps of determining isolated spatial areas and calculating weightedspatial relationships within the isolated spatial area.
 12. The datavisualization system of claim 7 further arranged to perform the steps ofcross tabulating the determined lift values and spatial performancevalues to show the relationship between each of the spatial elementswithin the predefined spatial areas.